Nonlinear reflection of an obliquely incident longitudinal wave at a free surface

F. A. Bender, J. Y. Kim, L. J. Jacobs, J. Qu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

The complete physical process of the nonlinear reflection of an incident P-wave from a stress-free boundary has been investigated analytically. The objective of this research is to evaluate the feasibility of using the second harmonic generation technique in reflection mode. The primary wave field consists of an incident plane P-wave and linearly reflected P- and SV-waves. Self- and cross-interaction of these primary waves generate secondary waves, which, together with the primary waves, produce the nonlinear stress field at the boundary. The involved nonlinear boundary value problem (BVP) is decomposed into two linear BVPs by perturbation and general solutions of them are given. The obtained solution for the secondary field shows that the generation of second harmonic waves in the bulk is strongly affected by the nonlinear stress field at the boundary. Changes in the second harmonic amplitudes upon the boundary reflection are calculated numerically for different angles of incidence for aluminum. The case of normal incidence is presented and compared to the more general case of oblique incidence.

Original languageEnglish
Title of host publicationReview of Progress in Quantitative Nondestructive Evaluation
Pages298-305
Number of pages8
DOIs
StatePublished - 2011
Event37th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE - San Diego, CA, United States
Duration: 18 Jul 201023 Jul 2010

Publication series

NameAIP Conference Proceedings
Volume1335
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference37th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE
Country/TerritoryUnited States
CitySan Diego, CA
Period18/07/1023/07/10

Keywords

  • Nonlinear Acoustics
  • Nonlinear Boundary Value Problem
  • Nonlinear Reflection
  • Perturbation Analysis
  • Second Harmonic Generation

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